The difference between a convertible bond and a bond with warrants is that

A$)$

a bond with warrants has an embedded put option, and a convertible bond has an embedded call option.

B$)$

when warrants are exercised, a portion of the issuer$$s debt is replaced with equity; when convertible bonds are exercised, a portion of the issuer$$s debt is replaced with equity.

C$)$

when warrants are exercised, the issuer receives equity capital from the warrants in addition to the original debt from the bond with warrants; when convertible bonds are converted, the bond is replaced with stock.

D$)$

a convertible bond has an embedded call option, and a bond with warrants does not.